How does one arrive at this equality?

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In summary, the conversation discusses the relationship between the Dirac delta, position and momentum eigenstates, and the path integral formulation. The equation \delta(q' - q) = \frac{1}{2\pi} \int dp e^{i p (q' - q)} is used to show this relationship, with p representing the set of momenta. The factor of \frac{1}{2\pi} is derived from the equation \langle q \mid p \rangle = e^{ipq}, which is mentioned later in the conversation. The speaker expresses confusion about the order of information presented and the lack of a professor to ask for clarification.
  • #1
Tac-Tics
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I'm reading about the path integral formulation.

How do you show that:

[tex]\delta(q' - q) = \frac{1}{2\pi} \int dp e^{i p (q' - q)}[/tex]

with δ as the Dirac delta, q and q' as two position eigenstates, and (I'm only guessing) p as an iterator over the set of momenta.

I'm not sure the relationship between q and p that makes this work and I'm also not sure where that [tex]\frac{1}{2 \pi}[/tex] factor comes from.
 
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  • #2
Ah, reading down half a page, they give the relationship:

[tex]\langle q \mid p \rangle = e^{ipq}[/tex]

I believe that's what I was looking for.

(I just wish they'd put this stuff in the right order! It's hard not having a professor to bug.)

(But I'm still unsure where that 1/2pi comes from).
 

1. How do you determine what values to use in the equation?

The values used in an equation are typically determined by the variables involved and the relationships between them. These variables can be derived from experiments, observations, or theoretical models.

2. What is the significance of the equal sign in an equation?

The equal sign in an equation signifies that the expressions on both sides are equivalent, or have the same value. This allows us to solve for unknown variables and make predictions based on known information.

3. Can an equation have more than one solution?

Yes, an equation can have more than one solution. This is known as multiple solutions or a solution set. It is important to check if all solutions are valid and relevant to the problem at hand.

4. How do you know if an equation is balanced?

An equation is considered balanced if the number of atoms of each element on both sides of the equation are equal. This is commonly referred to as the law of conservation of mass.

5. What are the different methods used to solve an equation?

There are several methods used to solve equations, such as substitution, elimination, graphing, and using matrices. The method used depends on the type of equation and the desired outcome.

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